On residually finite groups with Engel-like conditions

Abstract

Let $m,n$ be positive integers. Suppose that $G$ is a residually finite group in which for every element $x\in G$ there exists a positive integer $q=q(x)⩽m$ such that $x^q$ is $n$-Engel. We show that $G$ is locally virtually nilpotent. Further, let $w$ be a multilinear commutator and $G$ a residually finite group in which for every product of at most $896$ $w$-values $x$ there exists a positive integer $q=q(x)$ dividing $m$ such that $x^q$ is $n$-Engel. Then $w(G)$ is locally virtually nilpotent.

9 pages

References in corpus (1)

• On profinite groups with Engel-like conditions

Cited by in corpus (2)

• The non-abelian tensor square of residually finite groups
• Bounded Engel elements in residually finite groups